If you don’t have a catch-all address, email to addresses that aren’t set up will bounce. It doesn’t get stored anywhere.

Maybe? It’d really depend on the service. Many mail filtering services are likely to be difficult to use with a catch-all, as they will expect you to log in separately to view messages for each address mail was received at. (Some may even want you to pay for each address!)

It’s a little hard to say without knowing more about how you’re using your catch-all address. In general, though, I’d advise that you discontinue using catch-all addresses if at all possible. If there are a limited number of addresses that you actually receive mail at, for instance, I’d recommend that you set those up explicitly as forwards.